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In this paper, we present an approach we refer to as "least squares congealing" which provides a solution to the problem of aligning an ensemble of images in an unsupervised manner. Our approach circumvents many of the limitations existing in the canonical "congealing" algorithm. Specifically, we present an algorithm that:-(i) is able to simultaneously, rather than sequentially, estimate warp parameter updates, (ii) exhibits fast convergence and (iii) requires no pre-defined step size. We present alignment results which show an improvement in performance for the removal of unwanted spatial variation when compared with the related work of Learned-Miller on two datasets, the MNIST hand written digit database and the MultiPIE face database.